How can you solve something like this ? Find f'(-2) for f(x) = |x|.

[Sithira]

I have this function question:

\(\displaystyle \mbox{(i) Find }\, f'(-2)\, \mbox{ of the function }\, f(x)\, =\, |x|\)

i know this is easy but i have no idea how to ? any help ? like with steps and explanations would be great

 

[Deleted member 4993]

I have this function question:

\(\displaystyle \mbox{(i) Find }\, f'(-2)\, \mbox{ of the function }\, f(x)\, =\, |x|\)

i know this is easy but i have no idea how to ? any help ? like with steps and explanations would be great

If f(x) = |x|

what is f(x) when x > 0?

what is f(x) when x < 0?

similarly,

what is f'(x) when x > 0?

what is f'(x) when x < 0?

 

[HallsofIvy]

In other words, in order to find the derivative of a function, you first have to know what the function is! How is |x| defined?

(You could also use the fact that the derivative. at a point, is the slope at that point. What does the graph of y= |x| look like?)